Question

The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000. If the level of significance for this two-tailed test is 0.10, what is/are the critical value(s)

Answer 1

At the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Explanation:

We are given that the mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000.

The ship building association wishes to find out whether their welders earn more or less than $20,000 annually.

Let
`\mu` = mean gross annual incomes of certified welders

So, Null Hypothesis,
`H_0` :
`\mu` = $20,000

Alternate hypothesis,
`H_A` :
`\mu \\eq` $20,000

Here, null hypothesis states that the mean income of welders is equal to $20,000.

On the other hand, alternate hypothesis states that the mean income of welders is not $20,000.

Also, the test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample mean income

`\sigma` = population standard deviation = $2,000

n = sample size

Now, at the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.